Research interests
Convex Analysis
Optimization
Mathematical Programming
Variational Analysis
Numerical Methods
Publications
Preprints
Relationships between global and local monotonicity of operators
(with V.V.H. Khoa, J.E. Martinez-Legaz, and B. S. Mordukhovich)
https://arxiv.org/abs/2403.20227
Coderivative-based Newton methods in structured nonconvex and nonsmooth optimization
(with B. S. Mordukhovich and V. T. Phat)
https://arxiv.org/abs/2403.04262
Fundamental convergence analysis of sharpness-aware minimization
(with B. S. Mordukhovich, H.-C. Luong and D. B. Tran)
https://arxiv.org/abs/2401.08060
Second-order subdifferential optimality conditions in nonsmooth optimization
(with V. V. H. Khoa, B. S. Mordukhovich and V. T. Phat:)
https://arxiv.org/abs/2312.16277
Local minimizers of nonconvex functions in Banach spaces via Moreau envelopes
(with V. V. H. Khoa, B. S. Mordukhovich and V. T. Phat)
https://arxiv.org/abs/2311.18586
Variational and strong variational convexity in infinite-dimensional variational analysis
(with V. V. H. Khoa, B. S. Mordukhovich and V. T. Phat)
https://arxiv.org/abs/2309.13779
Local maximal monotonicity in variational analysis and optimization
(with V. V. H. Khoa, B. S. Mordukhovich and V. T. Phat)
https://arxiv.org/abs/2308.14193
General derivative-free optimization methods under global and local continuity of gradients
(with B. S. Mordukhovich and D. B. Tran)
https://arxiv.org/abs/2311.16850
Inexact proximal method for weakly convex functions
(with B. S. Mordukhovich, V. T. Phat and D. B. Tran)
https://arxiv.org/abs/2307.15596
Papers
2024
Globally convergent coderivativebased generalized Newton methods in nonsmooth optimization
(with B. S. Mordukhovich, V. T. Phat and D. B. Tran)
https://arxiv.org/abs/2109.02093
Mathematical Programming Series A, 205, 373-429, 2024
A new inexact gradient descent method with applications to nonsmooth convex optimization
(with B. S. Mordukhovich and D. B. Tran)
https://arxiv.org/abs/2303.08785
Optimization Methods and Software ,DOI: https://doi.org/10.1080/10556788.2024.2322700
2023
Inexact reduced gradient methods in nonconvex optimization
(with B. S. Mordukhovich and D. B. Tran)
https://arxiv.org/abs/2204.01806
Journal of Optimization Theory and Applications, DOI: 10.1007/s10957-023-02319-9 (2023)
Variational convexity of functions and variational sufficiency in optimization
(with B. S. Mordukhovich and V. T. Phat)
https://arxiv.org/abs/2208.14399
SIAM Journal on Optimization, 33, 1121–1158, 2023
Generalized damped Newton algorithms in nonsmooth optimization via second-order subdifferentials
(with B. S. Mordukhovich, V. T. Phat and D. B. Tran)
https://arxiv.org/abs/2101.10555
Journal of Global Optimization, 86, 93–122, 2023
Variational convexity of functions in Banach spaces
(with V. V. H. Khoa, B. S. Mordukhovich and V. T. Phat)
https://arxiv.org/abs/2212.06945
Functional Analysis and Continuous Optimization. J. M. Amigó, M. J. Cánovas et al. (eds.),
Springer Proceedings in Mathematics and Statistics, 424, 237–260, Springer, Cham, Switzerland, 2023
Proximal point algorithm for the generalized P0 variational inequalities
(with T.H. Mo, and H. P. Toan)
https://vjol.info.vn/index.php/sphcm/article/view/79375/67587
HCMUE Journal of Science, 20, 491–504, 2023
2022
A generalized Newton method for subgradient systems
(with B. S. Mordukhovich and V. T. Phat)
https://arxiv.org/abs/2009.10551
Mathematics of Operations Research, 48, 811-1845, 2022
Continuous Fr échet differentiability of the Moreau envelope of convex functions on Banach spaces
(with N. B. Tran)
Journal of Optimization Theory and Applications, 195, 1007–1018, 2022
Variational inequalities governed by strongly pseudomonotone operators
(with P. T. Kha)
https://arxiv.org/abs/1807.11292
Optimization, 71, 1983–2004, 2022
Convergence rate of a gradient projection method for solving variational inequalities.
(with P. T. Vuong and L. V. Vinh)
http://jnva.biemdas.com/issues/JNVA2021-6-8.pdf
Journal of Nonlinear and Variational Analysis, 5, 951–964, 2021
2021
Lipschitz continuity of convex functions
(with N. B. Tran)
https://arxiv.org/abs/1911.04886
Applied Mathematics & Optimization, 84, 1623–1640, 2021
2020
Faces and support functions for the values of maximal monotone operators
(with N. B. Tran)
https://arxiv.org/abs/1911.04892
Journal of Optimization Theory and Applications, 186, 843–863, 2020
Second-order characterizations of quasiconvexity and pseudoconvexity for differentiable functions with Lipschitzian derivatives
(with V. T. Phat)
https://arxiv.org/abs/1810.12783
Optimization Letters, 14(8), 2413–2427, 2020
2019
An alternative proof for the solution existence of finite-dimensional variational inequalities
(with H. P. Toan)
Linear and Nonlinear Analysis, 5, 299–304, 2019
Characterizations of nonsmooth robustly quasiconvex functions
(with B. T. Hoa and T. T. T. Trinh)
https://arxiv.org/abs/1804.06983
Journal of Optimization Theory and Applications, 180, 775–786, 2019
Necessary and sufficient conditions of qualitative properties in infinite-dimensional linear programming
(with T. H. Mo and T. T. T. Trinh)
Numerical Functional Analysis and Optimization, 40, 924–943, 2019
2018
Second-order characterizations of C1-smooth robustly quasiconvex functions
(with V. T. Phat)
Operations Research Letters, 46, 568–572, 2018
Error bounds for strongly monotone and Lipschitz continuous variational inequalities
(with B. N. Minh)
Optimization Letters, 12, 971–984, 2018
2017
Quasiconvex linear perturbations and convexity
(with M. Lassonde)
The American Mathematical Monthly, 123, 605-608, 2017
The Mordukhovich subdifferentials and directions of descent
(with J.-C. Yao and N. D. Yen)
Journal of Optimization Theory and Applications, 172, 518–534, 2017
Convergence rate of a modified extragradient method for pseudomonotone variational inequalities
Vietnam Journal of Mathematics, 45, 397–408, 2017
2016
A new extragradient method for strongly pseudomonotone variational inequalities
Numerical Functional Analysis and Optimization, 37, 1131–1143, 2016
Qualitative properties of strongly pseudomonotone variational inequalities
(with D. S. Kim and P. T. Vuong)
Optimization Letters, 10, 1669–1679, 2016
A modified extragradient method for infinite dimensional variational inequalities
Acta Mathematica Vietnamica, 41, 251–263, 2016
2015
On the Tikhonov regularization of affine pseudomonotone mappings
Optimization Letters, 8, 1325–1336, 2014
Modified projection method for strongly pseudomonotone variational inequalities.
(with P. T. Vuong)
Journal of Global Optimization, 58, 341–350, 2014
2013
Multivalued Tikhonov trajectories of general affine variational inequalities
(with N. T. T. Huong and N. D. Yen)
Journal of Optimization Theory and Applications, 158: 85–96, 2013
2012
Partial solution for an open question on pseudomonotone variational inequalities
Applicable Analysis, 91, 1691–1698, 2012